GB2266384A

GB2266384A - Optical modulator

Info

Publication number: GB2266384A
Application number: GB9308263A
Authority: GB
Inventors: Colin Stuart Aitchison
Original assignee: British Technology Group Ltd
Current assignee: BTG International Ltd
Priority date: 1992-04-21
Filing date: 1993-04-21
Publication date: 1993-10-27
Also published as: GB9308263D0; GB9208560D0

Abstract

An optical modulator in which an optical carrier wave is modulated with a microwave signal comprises an artificial transmission line including a cascade of lumped inductors and shunt capacitors.

Description

OPTICAL MODULATORS This invention relates to optical modulators and, in particular, to the use of artificial transmission lines as a means of modulating an optical carrier with a microwave signal.

The use of lumped circuit elements and microwave transmission lines as a means of modulating an optical carrier with a broadband microwave signal using an electrooptic material such as lithium niobate have as well as other materials been extensively examined in in recent years.

The use of the lumped circuit modulator imposes constraints on the bandwidth of the modulator because of the need to maintain the interaction region lumped (i.e. short compared with the microwave wavelength) and the practical constraint of a 50Q source and load environment.

Considerable interest has been expressed in microwave transmission line modulators, in which the interaction region is not small compared with the wavelength. Such arrangements suffer from the disadvantage that the phase velocities of the optical and microwave signals differ and the technique is of limited benefit since the bandwidth is constrained by this effect. A number of attempts have been made to overcome this effect such as phase reversal of the modulating signal or periodic loading of the transmission line by lumped capacitors.

These techniques, whilst giving useful results, still require microwave modulating voltages in the region of 5 volts which remains a disadvantage.

We have developed an alternative approach which automatically provides equality of phase velocity and effectively cascades a large number of lumped element modulating structures and thereby offers the potential of a reduced modulating voltage and consequently reduced modulating power.

According to the present invention there is provided an optical modulator comprising a cascade of lumped inductors and shunt capacitors The invention will now be particularly described with reference to the accompanying drawing in which: Figure 1 shows an artificial transmission line.

Referring to the drawing, a transmission line in accordance with a specific embodmient of the invention has properties that are different from a true transmission line. In particular the characteristic impedance is frequency dependent and can be expressed in terms of Zo# or ZoT where zoir = (L/C)05/(l-(fIfc)2) and ZoT = (L/C)0.5(1-(f/fC)2) (1) L and C are the series inductors and shunt capacitors and fc is the line cut off frequency given by the expression (XuLC)-1 .

Propagation down the line ceases at the cut off frequency. The phase constant, 13, of the line is related to L and C by the expression ss = 2 sin-1(f/fc) (2) In principle, to match an artificial line, the source and load impedance must be frequency dependent in accordance with equation (1). However, a frequency independent Zo, given by (L/C)05 can be used for the source and load impedance by connecting it to the line through the appropriate m-derived half-section, which has the property of transforming ZO to ZoT or Zion This arrangement transforms the characteristic impedance to ZO up to 0.9 of the cut off frequency.However, terminating in ZO makes ss proportional to f up to the same factor of the cut off frequency and we can write 13 = 2f/fC (3) Whereas the constituent component values for a true transmission are specified in unit length terms (e.g.

capacitance per unit length, inductance per unit length) the corresponding specification for the artificial transmission line is in terms of inductance and capacitance per section. This gives the opportunity to vary the phase velocity on the artificial transmission line by variation of component spacing.

It is possible to arrange that an artificial transmission line has the same phase velocity as an optical transmission line.

The phase velocity, va of the artificial transmission line is given by xa/ssa sections per second where #a is the radian frequency and 13a is the phase constant of the artificial line.

If we now assume that the artificial line contains N sections per metre then the phase velocity can be expressed as Xa/(Nssa) metres per second.

For an artificial transmission line 13a is equal to 2 sin~l(a/c) where #c is the line cut off frequency. Thus we obtain 13a = 2 sin-1(#a/#c) (4) so that the phase velocity becomes

For an artificial transmission line terminated in Zo this simplifies to xC/2N.

We now assume the optical phase velocity to be v0 and equating the two phase velocities we get an expression for N which is

For the Zo terminated section case this becomes N = c (7) 2vo or N = c 2c where nO is the optical refractive index and c is the velocity of light.

Thus, if we wish to equate the optical and microwave phase velocities in lithium niobate with a refractive index of 3 using an artificial transmission line of cut-off frequency equal to 30GHz we select N to be equal to 942 sections per metre. This corresponds to a length per section of approximately lmm.

Considering the maximum length of the associated shunt capacitance, forming the lumped interactive region, this should not exceed B/8. This corresponds to 0.43mm for an effective dielectric constant of 18.8.

Thus an arrangement of an artificial transmission line with shunt capacitors formed from deposited line sections 0.43mm long with interconnecting inductances, not deposited on the lithium niobate, so that the total section length is lmm, will result in an equality of phase velocity between the microwave modulating signal and the optical signal. Such a line, if loss-free, could be infinitely long, thereby, reducing the modulating voltage required to produce the required optical phase change.

The phase length of an artificial transmission line is equal to the sum of the phase constant and associated length of each section.

In the case of an optical modulator we wish to calculate the effective length of n sections of modulating artificial line each consisting of a length 1 where 1 is such that the individual modulating element is essentially lumped.

The total change in phase a due to the non linearity of a single electrooptical lumped modulator of length L is AssL where AssL = -#n r V L (9) G # where #ss is the change in phase constant.

For an artificial transmission line we wish to know the total change in phase due to the N sections in the line. There are two factors which must be taken into account in this calculation. They are the effect of loss on the artificial line and the effect of voltage variation with frequency on artificial line.

There is no need to take into account the difference in phase velocity between the microwave and optical signal, since this has been made substantially equal to zero.

We need first to calculate the real and imaginary components of the propagation constant, r, of the artificial transmission line. This is related to the series line elements, Z1, and shunt elements, Z2 by the expression cosh r = Z1 (10) 2Z2 Figure 1 shows Z1 and Z2 in our case and illustrates that 7 is loss free and equal to jxL whilst Z2 contains series loss equal to R so that Z2 equals R + C. This gives for r the expression cosh r = l /zj"2 C + Y2jco3 LC2R (11) If we assume that the real part of the propagation constant, a, is small then we can write cosh r = cos ss + jα;sinss which gives the expression

This yields the convenient approximation a = CR (co/coc) (13) It is convenient to use measured values of a to predict the performance of an artificial transmission line modulator.

A property of an artificial transmission line terminated in m-derived half-sections which are themselves terminated in a frequency independent impedance Zo (equal to (L/C)0.S) is that the line voltage, V(), is frequency dependent in accordance with the expression V(w) = V(O)/(l-co/coc )2)O.25 (14) where V(O) is the line voltage at low frequency.

The effect of this is that the voltage on the line increases with frequency. This is a useful feature as it tends to reduce the effect of loss associated with the line which diminishes the voltage across each modulator capacitance.

The total phase modulation, , produced by the modulating elements of the artificial transmission line is the sum of the individual contributions. We write b = #n r# (V1 11 + V2 12 ..Vrlr +. . .+ Vnln) (15) G# where n is the optical refractive index r is the appropriate component of the electrooptical tensor r is the overlap integral G is the modulating line gap X is the optical wavelength Vr is the line voltage on the rth modulator 1r is the length of the rth modulator.

If we write #ss for the first factor in the above expression and assume the modulator lengths are identical and equal to 1, we obtain the expression # = A13V1 1(1 + e-# + e-2# +. . . .+ e-(n-1)r (16) where r is the propagation constant

Since the optical and microwave phase velocities are identical the imaginary component of # is zero and we have

or

where leff is the effective length of the artificial line modulator.

We now wish to obtain a numerical value for a. A typical insertion loss for coplanar wave guide of appropriate dimensions of about ldB per cm -(GHz) which corresponds to a value of a in equation (18) of 0.0049-(GHz)3 for a 0.43mm long section.

Equation (18) can be simply approximated when both a and Na are small to give = A13V1Nl (19) This equation is significant in that it demonstrates that the effective length of the artificial line modulator at low frequencies is N times the length of the single lumped modulator. Thus the power requirement for a given phase change from the artificial line modulator is 1/N2 of the power requirement for a single lumped element modulator change.

More generally, without the assumption that a and Na are small and taking the increase in a with frequency into account by writing a = alb/2 (20) where B is the bandwidth expressed in GHz we can define a bandwidth which corresponds to a halving of the phase change compared with the low frequency value.

We write

The solution to this equation determines B and is a function N.

It is of interest to use measured values of a to predict bandwidth B. Assuming a lumped interactive length of 0.4mm and the previously quoted measured value for alteration of ldB per cm -(GHz)0-5 a value for N of 40 gives a bandwidth B of 64GHz.

An artificial transmission line optical modulator in accordance with the invention has the primary benefit that the phase velocity of the microwave modulating signal can be made numerically equal to that of the optical signal, thereby optimising the performance of the modulator.

In particular the phase change produced by the artificial line modulator with N sections is N times the phase change produced by a single section. Thus the modulation power of the artificial line modulator is 1/N2 of the single modulator power requirement for a given total phase change.

There are corresponding bandwidth benefits with a predicted bandwidth of 64GHz for a reduction in phase change by a factor of two assuming the use of 40 interactive sections which are designed to be lumped.

Claims

1. An optical modulator comprising an artificial transmission line including a cascade of lumped inductors and shunt capacitors

2. An optical modulator as claimed in claim 1 further including source and/or load matching means consisting of an m-derived half-section.

3. An optical modulator as claimed in either claim 1 or claim2 fabricated in lithium niobate.

4. An optical modulator as claimed in claim 3 including shunt capacitances forming lumped interactive regions of length less than one eighth of the cut-off wavelength of the device.